If ${ }^{(n-1)} C_3+{ }^{(n-1)} C_4>{ }^n C_3$,then the minimum value of $n$ is

How many words of $4$ consonants and $3$ vowels can be formed from $6$ consonants and $5$ vowels?

$^{47}C_4 + \sum_{r=1}^5 {}^{52-r}C_3 = $

$A$ student has to answer $10$ out of $13$ questions in an examination,choosing at least $5$ questions from the first $6$ questions. The number of choices available to the student is:

If $^{15}C_{3r} = ^{15}C_{r+3}$,then the value of $r$ is

Determine $n$ if $^{2n}C_{3} : ^{n}C_{3} = 11 : 1$.